职前教师数学观发展研究：数学史的视角

发布时间：2018-05-28 04:22

本文选题：职前教师 + 数学观　；参考：《华东师范大学》2017年博士论文

【摘要】：近几十年来,数学教学的研究焦点发生了重要转变,由传统的聚焦于教师与学生的行为转移到考察教师与学生所具有的知识以及数学观。许多研究表明,个体持有的数学观影响着个体的数学教学或者数学学习。本研究的对象是职前教师,主要限定于师范院校数学课程与教学论以及学科教学(数学)方向的硕士研究生;研究的目的则是探究如何利用数学史来发展职前教师的数学观。本研究将理论思辨研究与实证研究结合了起来。在理论探讨部分,通过对以往研究的梳理,对职前教师的数学世界进行了分析,并在此基础上界定了职前教师数学观的内涵,以及构建了考察职前教师数学观的一个理论框架;在实证研究部分,根据之前所得到的理论框架,通过设计研究的方法,对利用数学史来发展职前教师数学观的路径进行了探索。在本研究中,主要采用的研究方法是设计研究。其中,设计研究的目的是丰富职前教师的数学世界、发展职前教师的数学观,设计的对象则是《数学发展史》课程的整体定位、课程理念以及内容选择。本研究中的设计研究共进行了两轮,每一轮均有如下四个阶段:调研与准备阶段、开发与设计阶段、执行与操作阶段、分析与评价阶段,最后得到了职前教师数学观的发展路径以及促进职前教师数学观发展的机制。通过研究,得到了以下结论:一、《数学发展史》这一课程选择从初等数学到大学数学作为反思讨论的主要内容,提供关于这些内容的主客观性知识,并兼顾数学史的丰富性以及数学家的深刻性,则该课程可以丰富职前教师的数学世界、促进职前教师数学观的发展。二、《数学发展史》这一课程促进职前教师数学观的发展的内在机制是:该课程在丰富职前教师关于数学的主客观性知识基础上,提升了他们对于数学的认识,从而促进了职前教师数学观的发展。本研究主要得到了以下几个方面的成果:一、提出了职前教师数学世界的结构,并在此基础上界定了职前教师的数学观以及构建了考察职前教师数学观的一个理论框架。二、得到了利用数学史来发展职前教师数学观的发展路径,包括《数学发展史》这一课程的整体定位、课程理念和内容选择。三、得到了《数学发展史》这一课程促进职前教师数学观发展的内在机制。
[Abstract]:In recent decades, the research focus of mathematics teaching has changed from the traditional focus on the behavior of teachers and students to the investigation of teachers and students' knowledge and mathematics view. Many studies have shown that the view of mathematics held by individuals affects the mathematics teaching and learning of individuals. The object of this study is pre-service teachers, which are mainly limited to the postgraduates of mathematics curriculum and teaching theory in normal colleges and the direction of subject teaching (mathematics), while the purpose of the research is to explore how to use the history of mathematics to develop the mathematics view of pre-service teachers. This study combines theoretical speculative research with empirical research. In the part of theoretical discussion, the author analyzes the mathematics world of pre-service teachers by combing the previous research, and defines the connotation of mathematics view of pre-service teachers, and constructs a theoretical framework to investigate the mathematics view of pre-service teachers. In the part of empirical research, according to the previous theoretical framework, through the design of research methods, to explore the use of mathematical history to develop pre-service teachers' view of mathematics path. In this study, the main research method is design research. Among them, the purpose of design research is to enrich the mathematics world of pre-service teachers, and to develop the mathematics view of pre-service teachers. The object of design is the overall orientation, curriculum concept and content selection of the curriculum of the History of Mathematical Development. There are two rounds of design research in this study, each of which has the following four stages: research and preparation, development and design, execution and operation, analysis and evaluation. Finally, the development path of pre-service teachers' mathematics concept and the mechanism to promote the development of pre-service teachers' mathematics view are obtained. The main conclusions are as follows: first, the course from elementary mathematics to college mathematics is chosen as the main content of reflection discussion, and the subjective and objective knowledge about these contents is provided. Taking into account the richness of mathematics history and the profundity of mathematicians, the course can enrich the mathematics world of pre-service teachers and promote the development of mathematics views of pre-service teachers. Second, the inherent mechanism of the curriculum to promote the development of pre-service teachers' view of mathematics is that the course has enhanced their understanding of mathematics on the basis of enriching the subjective and objective knowledge of pre-service teachers about mathematics. Thus, it promotes the development of teachers' mathematics view. The main achievements of this study are as follows: first, the structure of pre-service teachers' mathematics world is put forward, and on the basis of this, the pre-service teachers' mathematical view is defined and a theoretical framework is constructed to examine the pre-service teachers' mathematical views. Secondly, the author obtains the way to develop the mathematics view of pre-service teachers by using the history of mathematics, including the overall orientation of the course "History of Mathematical Development", the course idea and the choice of content. Thirdly, the course of the history of mathematics development promotes the development of pre-service teachers' view of mathematics.
【学位授予单位】：华东师范大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：G643

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